Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (Memoirs of the American Mathematical Society)

Generalized Noncrossing Partitions and Combinatorics of Coxeter Groups (Memoirs of the American Mathematical Society)

By: Drew Armstrong (author)Paperback

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Description

This memoir is a refinement of the author's PhD thesis - written at Cornell University (2006). It is primarily a description of new research but also includes a substantial amount of background material. At the heart of the memoir the author introduces and studies a poset $NC^{(k)}(W)$ for each finite Coxeter group $W$ and each positive integer $k$. When $k=1$, his definition coincides with the generalized noncrossing partitions introduced by Brady and Watt in $K(\pi, 1)$'s for Artin groups of finite type and Bessis in The dual braid monoid. When $W$ is the symmetric group, the author obtains the poset of classical $k$-divisible noncrossing partitions, first studied by Edelman in Chain enumeration and non-crossing partitions.

Contents

Introduction; Coxeter groups and noncrossing partitions; $k$-divisible noncrossing partitions; The classical types; Fuss-Catalan combinatorics; Bibliography.

Product Details

  • ISBN13: 9780821844908
  • Format: Paperback
  • Number Of Pages: 159
  • ID: 9780821844908
  • ISBN10: 0821844903

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